| 求常系数线性齐次微分方程组初积分的待定系数法 |
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| 引用本文： | 黄光谷. 求常系数线性齐次微分方程组初积分的待定系数法[J]. 华中师范大学学报(自然科学版), 1987, 26(3): 0-0 |
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| 作者姓名： | 黄光谷 |
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| 作者单位： | 华中师范大学数学系 |
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| 摘 要： | 本文利用待定系数法得到一个结果:将求dX/dt=AX的初积分的问题,归结为求A′的特征值及特征向量系的问题;并且介绍了利用解二次方程组确定待定系数的方法。从而为解方程组dX/dt=AX及求其初积分提供了较简便的方法。
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| 关 键 词： | 可积组合 初积分 特征根 特征子空间 特征向量系 Jacobi行列式 通积分 |
| 收稿时间： | 1987-03-25 |
THE METHOD OF UNDETERMINED COEFFCIENTS USED TO FIND THE FIRST INTEGRAL OF A SYSTEM OF HOMOGENEOUS LINEAR ORDINARY DIFFERENTIAL EQUATIONS WITH CONSTANT COEFFICENTS |
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| Huang Guanggu. THE METHOD OF UNDETERMINED COEFFCIENTS USED TO FIND THE FIRST INTEGRAL OF A SYSTEM OF HOMOGENEOUS LINEAR ORDINARY DIFFERENTIAL EQUATIONS WITH CONSTANT COEFFICENTS[J]. Journal of Central China Normal University(Natural Sciences), 1987, 26(3): 0-0 |
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| Authors: | Huang Guanggu |
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| Affiliation: | Department of Mathematics |
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| Abstract: | In this paper, by using the method of undetermined coefficients we obtain the following: The problem of finding first integrals of dx/dt=AX is resulted in the problem of finding the characteristic values and characteristic systems of A';and introduce the method of finding the undetermined coefficients by solving a system of quadratic equations; thus provide a simple method of solving dx/dt=AX and finding its first integrals. |
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| Keywords: | integrable combination first integral characteristic roots characteristic subspace characteristic vector-system Jacobi determinant general integral |
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